Cumulative Sum Schemes for Monitoring the Ratio of Two Correlated Normal Variables in Short Production Runs with Fixed and Variable Sampling Interval Strategies: Application in Wheat Seed Processing

Short-run production is frequently used in manufacturing due to technological advancements, and it is integral to Agriculture 4.0. In addition, monitoring multiple variables in short production runs (SPR) is often essential. For example, balancing the ratio of coating components of wheat seeds is crucial for the growth and yield of wheat. Therefore, in this paper, two one-sided cumulative sum (CUSUM) schemes for monitoring the ratio of two correlated normal variables in SPR are proposed. Furthermore, performance metrics are evaluated, and the effects of various parameters on the schemes are analyzed through Monte Carlo simulations. To improve the detection efficiency of the proposed schemes, variable sampling interval (VSI) strategy is considered. The performance of these schemes under different sampling intervals is simulated. The results indicate that the monitoring performances of the schemes utilizing the VSI strategy surpass that of both the system without the VSI strategy and the Shewhart scheme. A comprehensive sensitivity analysis was conducted on the VSI strategy scheme to ensure its robustness. The analysis examined the effects of parameter variations, data contamination, and data correlation on the scheme’s performance. The proposed schemes were applied to the experiment of monitoring the nutrient composition ratio of wheat seed coating, and the results show that the schemes achieved the anticipated monitoring performance and possess practical application value.